32 ideas
22366 | There is no objectivity in social sciences - only viewpoints for selecting and organising data [Weber] |
Full Idea: There is no absolutely objective scientific analysis of 'social phenomena' independent of special and 'one-sided' viewpoints according to which expressly or tacitly, consciously or unconsciously they are selected and organised for expository purposes. | |
From: Max Weber ('Objectivity' in Social Sciences and Social Policy [1904], p.72), quoted by Reiss,J/Spreger,J - Scientific Objectivity 5.1 | |
A reaction: Weber urged some objectivity by not judging agents' goals. Also see Idea 22367 |
22367 | The results of social research can be true, and not just subjectively valid for one person [Weber] |
Full Idea: Cultural sciences do not have results which are 'subjective' and only valid for one person and not others. ...For scientific truth is precisely what is valid for all who seek the truth. | |
From: Max Weber ('Objectivity' in Social Sciences and Social Policy [1904], p.84), quoted by Reiss,J/Spreger,J - Scientific Objectivity 5.1 | |
A reaction: Weber said that although research interests are subjective, the social causes discovered can be objective. |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
Full Idea: A proof of the consistency of propositional logic was given by Emil Post in 1921. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2.1) |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
Full Idea: Propositional language is very rudimentary and has limited powers of expression. The only relation between various statements it can handle is that of identity and difference. As are all the same, but Bs can be different from As. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 7 Intro) | |
A reaction: [second sentence a paraphrase] In predicate logic you could represent two statements as being the same except for one element (an object or predicate or relation or quantifier). |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
Full Idea: Boolean connectives are interpreted as functions on the set {1,0}. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 5.1) | |
A reaction: 1 and 0 are normally taken to be true (T) and false (F). Thus the functions output various combinations of true and false, which are truth tables. |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
Full Idea: The empty set is mainly a mathematical convenience - defining a set by describing the properties of its members in an involved way, we may not know from the very beginning what its members are. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
Full Idea: Without the assumption of the empty set, one would often have to take special precautions for the case where a set happened to contain no elements. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) | |
A reaction: Compare the introduction of the concept 'zero', where special precautions are therefore required. ...But other special precautions are needed without zero. Either he pays us, or we pay him, or ...er. Intersecting sets need the empty set. |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
Full Idea: Ordinals play the central role in set theory, providing the paradigmatic well-orderings. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
A reaction: When you draw the big V of the iterative hierarchy of sets (built from successive power sets), the ordinals are marked as a single line up the middle, one ordinal for each level. |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
Full Idea: In order to construct precise and valid patterns of arguments one has to determine their 'building blocks'. One has to identify the basic terms, their kinds and means of combination. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], History Intro) | |
A reaction: A deceptively simple and important idea. All explanation requires patterns and levels, and it is the idea of building blocks which makes such things possible. It is right at the centre of our grasp of everything. |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
Full Idea: A specification of a domain of objects, and of the rules for interpreting the symbols of a logical language in this domain such that all the theorems of the logical theory are true is said to be a 'model' of the theory. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.1.3) | |
A reaction: The basic ideas of this emerged 1915-30, but it needed Tarski's account of truth to really get it going. |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
Full Idea: The L-S Theorem is ...a shocking result, since it implies that any consistent formal theory of everything - even about biology, physics, sets or the real numbers - can just as well be understood as being about natural numbers. It says nothing more. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2) | |
A reaction: Illuminating. Particularly the point that no theory about the real numbers can say anything more than a theory about the natural numbers. So the natural numbers contain all the truths we can ever express? Eh????? |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
Full Idea: Having such a compact [axiomatic] presentation of a complicated field [such as Euclid's], makes it possible to relate not only to particular theorems but also to the whole field as such. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
Full Idea: Axiomatic systems, their primitive terms and proofs, are purely syntactic, that is, do not presuppose any interpretation. ...[142] They never address the world directly, but address a possible semantic model which formally represents the world. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
Full Idea: The collection of ordinals is defined inductively: Basis: the empty set is an ordinal; Ind: for an ordinal x, the union with its singleton is also an ordinal; and any arbitrary (possibly infinite) union of ordinals is an ordinal. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
A reaction: [symbolism translated into English] Walicki says they are called 'ordinal numbers', but are in fact a set. |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
Full Idea: An ordinal can be defined as a transitive set of transitive sets, or else, as a transitive set totally ordered by set inclusion. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
Full Idea: Every member of an ordinal is itself an ordinal, and every ordinal is a transitive set (its members are also its subsets; a member of a member of an ordinal is also a member of the ordinal). | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
Full Idea: We can form infinite ordinals by taking unions of ordinals. We can thus form 'limit ordinals', which have no immediate predecessor. ω is the first (the union of all finite ordinals), ω + ω = sω is second, 3ω the third.... | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
Full Idea: There may be several ordinals for the same cardinality. ...Two ordinals can represent different ways of well-ordering the same number (aleph-0) of elements. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
A reaction: This only applies to infinite ordinals and cardinals. For the finite, the two coincide. In infinite arithmetic the rules are different. |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
Full Idea: Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
Full Idea: Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1) | |
A reaction: There has to be an well-founded ordering for inductive proofs to be possible. |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
Full Idea: The link between time and modality was severed by Duns Scotus, who proposed a notion of possibility based purely on the notion of semantic consistency. 'Possible' means for him logically possible, that is, not involving contradiction. | |
From: Michal Walicki (Introduction to Mathematical Logic [2012], History B.4) |
7082 | Nature requires causal explanations, but society requires clarification by reasons and motives [Weber, by Critchley] |
Full Idea: Weber coined the distinction between explanation and clarification, saying that natural phenomena require causal explanation, while social phenomena require clarification by giving reasons or offering possible motives for how things are. | |
From: report of Max Weber (works [1905]) by Simon Critchley - Continental Philosophy - V. Short Intro Ch.7 | |
A reaction: This is music to the ears of property dualists and other non-reductivists, but if you go midway in the hierarchy of animals (a mouse, say) the distinction blurs. Weber probably hadn't digested Darwin, whose big impact came around 1905. |
1757 | The Electra: she knows this man, but not that he is her brother [Eucleides, by Diog. Laertius] |
Full Idea: The 'Electra': Electra knows that Orestes is her brother, but not that this man is Orestes, so she knows and does not know her brother simultaneously. | |
From: report of Eucleides (fragments/reports [c.410 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Eu.4 | |
A reaction: Hence we distinguish 'know of', 'know that' and 'know how'. Hence Russell makes 'knowledge by acquaintance' fundamental, and descriptions come later. |
22155 | We are disenchanted because we rely on science, which ignores values [Weber, by Boulter] |
Full Idea: Weber contends that modern western civilisation is 'disenchanted' because our society's method of arriving at beliefs about the world, that is, the sciences, is unable to address questions of value. | |
From: report of Max Weber (works [1905]) by Stephen Boulter - Why Medieval Philosophy Matters 6 | |
A reaction: This idea, made explicit by Hume's empirical attitude to values, is obviously of major importance. For we Aristotelians values are a self-evident aspect of nature. Boulter says philosophy has added to the disenchantment. I agree. |
3028 | The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides] |
Full Idea: The chief good is unity, which is known by several names, for at one time people call it prudence, at another time God, at another intellect, and so on. | |
From: Eucleides (fragments/reports [c.410 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.9.2 |
20725 | The idea of duty in one's calling haunts us, like a lost religion [Weber] |
Full Idea: The idea of duty in one's calling prowls about in our lives like the ghost of dead religious beliefs. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
A reaction: Great sentence! Vast scholarship boiled down to a simple and disturbing truth. I recognise this in me. Having been 'Head of Philosophy' once is partly what motivates me to compile these ideas. |
21132 | Domination is probable obedience by some group of persons [Weber] |
Full Idea: Domination is the probability that a command with a specific content will be obeyed by a given group of persons. | |
From: Max Weber (Economy and Society [1919], p.53), quoted by Andrew Shorten - Contemporary Political Theory 06 | |
A reaction: Said to be an 'influential definition'. In principle you might have no domination, but be regularly obeyed because your commands were so acceptable to a very independent-minded group of people. That said, good definition! |
20722 | Acquisition and low consumption lead to saving, investment, and increased wealth [Weber] |
Full Idea: If people are acquisitive but consumption is limited, the inevitable result is the accumulation of capital through the compulsion to save. The restraints on consumption naturally served to increase wealth by enabling the productive investment of capital. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
A reaction: [compressed. He also quotes John Wesley saying this] In a nutshell, this is how the protestant ethic (esp. if puritan) drives capitalism. It also needs everyone to have a 'calling', and a rebellion against monasticism in favour of worldly work. |
20724 | When asceticism emerged from the monasteries, it helped to drive the modern economy [Weber] |
Full Idea: When asceticism was carried out of the monastic cells into everyday life, and began to dominate worldly morality, it did its part in building the tremendous cosmos of the modern economic order. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 5) | |
A reaction: Since Max Weber's time I should think this is less and less true. If you hunt for ascetics in the modern world, they are probably dropped out, and pursuing green politics. Industrialists are obsessed with property and wine. |
20717 | Capitalism is not unlimited greed, and may even be opposed to greed [Weber] |
Full Idea: Unlimited greed for gain is not in the least identical with capitalism, and is still less in its spirit. Capitalism may even be identical with the restraint, or at least a rational tempering, of this irrational impulse. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], Author's Intro) | |
A reaction: The point is that profits have to be re-invested, rather than spent on pleasure. If we are stuck with capitalism we need a theory of Ethical Capitalism. |
20718 | Modern western capitalism has free labour, business separate from household, and book-keeping [Weber] |
Full Idea: The modern Occident has developed a very different form of capitalism: the rational capitalist organisation of free labour …which needed two other factors: the separation of the business from the household, and the closely connected rational book-keeping. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], Author's Intro) | |
A reaction: For small businesses the separation has to be maintained by a ruthless effort of imagination. Book-keeping is because the measure of loss and profit is the engine of the whole game. Labour had to be dragged free of family and community. |
20719 | Punish the heretic, but be indulgent to the sinner [Weber] |
Full Idea: The rule of the Catholic church is 'punishing the heretic, but indulgent of the sinner'. | |
From: Max Weber (The Protestant Ethic and the Spirit of Capitalism [1904], 1) | |
A reaction: Weber cites this as if it is a folklore saying. It seems to fit the teachings of Jesus, who is intensely keen on unwavering faith, but very kind to those who stray morally. Hence Graham Greene novels, all about sinners. |